Electronics & Electrical Engineering

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# Microwave Active Circuit Analysis and Design

The modern world as we know it would be unimaginable without radio frequency and microwave electronics. Cellular phones, satellite navigation, Wi-Fi, even the humble car locking key-fob all owe their existence to a body of theoretical knowledge and practical designs, relating to electromagnetic fields and high frequency electronics, that has been built up over the past 150 years or so. The importance of radio frequency technology is only set to increase in the future, as we move towards higher and higher operating frequencies for all kinds of electronic devices and systems. Microprocessors now have clock frequencies in the GHz frequency range, making them technically “microwave” devices, and radio communications device technology is now approaching the Terahertz (1,000 GHz) region. The range of applications of radio frequency (RF) electronics is also set to widen, as mobile networks enter the 5th generation and we enter the era of the Internet of Things. These developments will certainly require more and more information bandwidth to be made available, which can only be achieved by moving to higher bit rates, wider signal bandwidths and higher and higher radio frequencies. A basic understanding of microwave components and circuitry will therefore become an increasingly important part of any modern electronic engineering course.

To meet this need, we have drawn upon our 50 years combined experience in microwave and radio communications education and industry to produce a book that brings together the foundational elements of this discipline in one comprehensive text. Although there are already several notable and influential books covering the field of microwave circuit design, many of these are too narrowly focused to be suitable for general teaching and learning. Our goal in writing this book is to provide a readable learning resource that starts with the fundamentals and then leads the reader step-by-step towards a deeper understanding of key microwave circuit design concepts. The book is aimed at undergraduate and postgraduate students, and also the self-taught practicing engineer.

Due to spectacular advances in semiconductor technology over recent decades, microwave active circuit technology has tended to evolve far more rapidly than that of purely passive microwave components such as filters, isolators and so on. Our book therefore concentrates on active microwave circuit design, although we do cover the design of passive matching networks, for example, since they are essential to the design of contemporary active circuits such as amplifiers, oscillators and mixers.

The widespread availability of powerful Computer Aided Design (CAD) software has boosted the productivity of microwave design work enormously, allowing rapid optimization of complex circuits and eliminating hours of demanding “bench time”. The widespread availability of low cost computer power, however, does present a potential challenge for engineering education in that students may be tempted to cut out the design phase and go straight from concept to simulation. With this in mind, we chose to focus on the development of insight and understanding, using examples and problems that do not rely on CAD software for their solutions. The knowledge thus gained can then be applied in the context of any CAD package the reader chooses to use.

The book is structured in modular form to facilitate its use in teaching and independent learning. Each chapter may be considered as forming the basis of a 2 to 3-hour lecture, and a set of lecture notes covering the chapter topic is available for instructors to download from the companion website. The 17 chapters are organized into three sections, covering foundations, analysis and design topics. Each chapter begins with a list of the key learning outcomes, in terms of knowledge to be gained and skills to be acquired. At the end of each chapter the salient points of the chapter are summarized in the form of list of ‘take-aways’.

The “foundations” section (chapters 1 to 4) addresses the core knowledge that any practicing microwave engineer would be expected to possess, such as the properties of materials and the behavior of components at microwave frequencies, Q factors, maximum power transfer and basic microwave metrics. Some of these topics will be familiar revision for those having an general undergraduate electronics background. The Foundations section also covers the important area of transmission line theory, contemporary transmission line technologies, such as microstrip and coplanar waveguide, and the theory and application of the Smith Chart.

One of the key learning objectives of the foundations section is for the students to understand that, at shorter wavelengths, even a humble piece of connecting wire becomes a transmission line with reactive characteristics. For circuits with physical dimensions of a few centimetres, therefore, we need to consider the electrical length of connecting wires when the frequency of operation is more than a few hundred MHz. If the frequency range is in the tens of GHz then the electrical length will be around 1 mm or less (i.e. “sub-millimeter”). This phenomenon distinguishes microwave circuit design apart from circuit design methodologies used at lower frequencies, where electrical length can normally be safely ignored. The approach to teaching transmission line theory and practice adopted in chapters 2 and 3 is to start by describing the behaviour of pulses travelling on transmission lines. It is our belief that this approach is more accessible for readers encountering these concepts for the first time. We then proceed to a more traditional approach to describing the behaviour of sinusoidal signals on transmission lines, allowing us to introduce concepts such as standing wave ratio and reflection coefficient.

The “analysis” section (chapters 5 to 10) covers various techniques of circuit analysis as they apply specifically to active circuits. We explain the theory and application of immittance parameters and S-parameters, and how they are inter-related. A whole chapter (chapter 7) is devoted to gain and stability of two-port networks, concepts that are of critical importance when dealing with active devices. We have observed that the correct definition of power gain can often be the source of confusion for students, so we have paid special attention to explaining this topic clearly and comprehensively. Two other chapters in this part cover the analysis (as well as the design) of matching networks, which, although themselves passive circuits, are essential determinants in the performance of many active microwave circuits such as amplifiers oscillators and mixers. Uniquely, this book includes a chapter detailing three-port network analysis of active circuits, a topic that is rarely found in other textbooks. We consider this as an important topic because the most commonly used active devices used today, namely transistors, are three terminal devices, and the application of three-port analysis techniques allows the microwave engineer additional degrees of freedom in the design process. It is in this chapter that the interesting and useful property of negative resistance in transistors is covered in some detail, and some original design techniques are introduced. Negative resistance is an essential prerequisite of many oscillator circuits and is also used in the design of reflection amplifiers. We introduce the reader to an original approach to determining the optimum feedback terminations needed to generate negative resistance a transistor using feedback.

The “design” section (chapters 11 to 17) begins with an introduction to the various types of semiconductor devices used in microwave circuits and how these are integrated in monolithic form. It then goes on to discuss the design of the most important system building blocks, namely amplifiers, oscillators and mixers. Due to the importance of noise in microwave systems, two chapters have been included that deal specifically with noise in amplifiers and oscillators, and design techniques that can be taken to minimize noise in the design phase. Modern developments in active microwave circuit topology, such as distributed amplifiers, cross-coupled oscillators and active mixers are explained in some detail. The material on distributed amplifiers in section 13.5.3 is an accessible introduction to this complex topic for the first time reader. By way of an illustrative example of the superior gain/bandwidth product of the distributed amplifier topology, the widest bandwidth amplifier so far implemented in monolithic microwave integrated circuit (MMIC) form, having a gain of 16dB over a frequency range of 253GHz, is described in section 12.9.

A number of worked examples of low noise amplifier design are provided , such as example 14.1 on page 491 and 14.2 on page 494, to illustrate the design techniques covered in chapter 14. In the context of multistage low noise amplifier design, the definition and application of the quantity known as “noise measure” is also covered in chapter 14 more extensively than in most other textbooks in this field. Noise measure (rather than noise figure) is the parameter that needs to be optimized for each stage when designing a multi-stage amplifier in order to achieve minimum overall noise figure. The book presents unique equations for circles of constant noise measure in section 14.6.1 and shows how they are applied in example 14.4 on page 505, where they are used to calculate the minimum noise measure for a transistor amplifier stage and the associated source termination.

In summary, we believe this book will be a valuable teaching and learning resource for students and practicing engineers alike. We have attempted to lead the reader, in a step-by-step manner, from the basics of the topic through to the most up-to-date implementations. Each chapter is designed to be delivered as a stand-alone lecture of 2 to 3 hours, and the availability of supporting lecture slides, examples and solutions make it an ideal basis for any taught course in microwave circuit design.

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**About the Authors**

**Izzat Darwazeh **is the Chair of Communications Engineering in University College London (UCL) and head of UCL’s Communications and Information Systems Group. He is an electrical engineering graduate of the University of Jordan and holds MSc and PhD degrees from the University of Manchester in the UK. He has been teaching and active in microwave circuit design and communications circuits and systems research since 1991. He currently teaches mobile and wireless communications and circuit design and his current research interests are in ultra high-speed microwave circuits and in wireless and optical communication systems. In addition to his teaching, Professor Darwazeh acts as a consultant to various engineering firms and government, financial and legal entities in the UK and worldwide. Professor Darwazeh is a Chartered Engineer and Fellow the Institute of Engineering and Technology (FIET).

**Clive Poole** is a Principal Teaching Fellow and Director of Telecommunications Industry Programmes at University College London (UCL). He has 30 years’ experience in the global electronics and telecommunications industries as well as academia. He started his career as a design engineer in several UK microwave companies, designing X-band and Ku-band amplifiers and oscillators for military and telecommunications applications. In the early 1990’s he founded an electronics design consultancy in Hong Kong that developed a number of successful wireless and telecommunications products for Chinese manufacturers. He has run several high technology businesses and was a pioneer in the business of deploying mobile phone networks on ocean going passenger ships.

Dr Poole’s teaching is focused in the areas of electronic and microwave circuit design, wireless and mobile communications, technology business strategy and finance. He holds a BSc degree in Electronic Engineering and MSc and PhD degrees in microwave engineering from the University of Manchester. He also holds an MBA from the Open University. Dr Poole is a Chartered Engineer and Fellow the Institute of Engineering and Technology (FIET).

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